具有时变阻尼的半线性波动方程经典解的寿命

Pub Date : 2023-06-01 DOI:10.4208/jpde.v36.n3.1

F. Guo, Jinling Liang null, Changwang Xiao

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引用次数: 0

摘要

．研究一类具有时变阻尼的半线性波动方程的柯西问题。在空间维数n = 1且非线性幂大于2的情况下，统一地研究了该问题经典解的寿命(cid:101) T (ε)和整体存在性。更准确地说，对于依赖于时间相关阻尼和非线性项的指标K的不同值，寿命(cid:101) T (ε)可以用ε−p 1−K, e ε−p或+∞来估计，其中ε是初始数据的紧支持的尺度。

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Life-Span of Classical Solutions to a Semilinear Wave Equation with Time-Dependent Damping

. This paper is concerned with the Cauchy problem for a semilinear wave equation with a time-dependent damping. In case that the space dimension n = 1 and the nonlinear power is bigger than 2, the life-span (cid:101) T ( ε ) and global existence of the classical solution to the problem has been investigated in a unified way. More precisely, with respect to different values of an index K , which depends on the time-dependent damping and the nonlinear term, the life-span (cid:101) T ( ε ) can be estimated below by ε − p 1 − K , e ε − p or + ∞ , where ε is the scale of the compact support of the initial data.

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